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Topic: equivalence of truth of Riemann hypothesis
Replies: 13   Last Post: Mar 1, 2014 11:10 AM

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 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: equivalence of truth of Riemann hypothesis
Posted: Jan 5, 2013 12:51 PM

On Sat, 5 Jan 2013 08:30:50 -0800 (PST), Jean Dupont
<jeandupont115@gmail.com> wrote:

>Op zaterdag 5 januari 2013 17:06:11 UTC+1 schreef David Bernier het volgende:
>> On 01/05/2013 09:55 AM, Jean Dupont wrote:
>>

>> > In the book "Math goes to the movies" it is stated that the truth of the Riemann hypothesis is equivalent to the following statement:
>>
>> > $\exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)$
>>
>> >
>>
>> > Is this correct?
>>
>> >
>>
>> > thanks
>>
>> > jean
>>
>>
>>
>> The movie "A Beautiful Mind" about John Nash is now on Youtube:
>>
>>
>>
>>
>>
>>
>> I think John Nash in the movie or in reality tried to make
>>
>> head-way on the Riemann Hypothesis ...
>>
>>
>>
>> David Bernier
>>
>>
>>
>> P.S. I'm afraid I can't read Tex or Latex ...

>just copy/paste the line
>
>exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)
>
>in the box shown on the following web page and press render:
>http://itools.subhashbose.com/educational-tools/latex-renderer-n-editor.html

When in Rome... If someone's going to read the TeX you posted, the
fact that it's TeX instead of text just makes it harder to read. You
shouldn't expect people to take the trouble to render your posts

|pi(x) - li(x)| <= C sqrt(x)/log(x) .

Simple. Perfectly clear.

>>
>jean
>>
>>
>> But, please see "error term" in Prime Number Theorem, here:
>>
>>
>>
>> primepages, 1901 von Koch result:
>>
>>
>>
>> < http://primes.utm.edu/notes/rh.html >
>>
>>
>>
>> I trust PrimePages. Also, Schoenfeld(1976) explicit bound:
>>
>>
>>
>> < http://en.wikipedia.org/wiki/Riemann_hypothesis > .

Date Subject Author
1/5/13 David Bernier
1/5/13 Jean Dupont
1/5/13 David C. Ullrich
1/5/13 Jean Dupont
1/6/13 David C. Ullrich
1/5/13 David Bernier
1/5/13 Jean Dupont
1/7/13 AP
3/1/14 Brian Q. Hutchings
1/20/13 Luis A. Rodriguez
1/20/13 Luis A. Rodriguez
2/28/14 kraflyn@gmail.com
3/1/14 Christopher J. Henrich